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zaharov [31]
3 years ago
15

At its highest​ point, the elevation of a county is 5,764 feet above sea level. At its lowest​ point, the elevation of the count

y is 7 feet below sea level. Answer parts a through c. a. Write an expression using integers to represent the difference between the elevations.
Mathematics
1 answer:
Feliz [49]3 years ago
8 0

Answer:

Difference = 5757\ feet

Step-by-step explanation:

Given

Highest\ Point = 5764\ feet

Lowest\ Point = 7\ feet

Required

Determine the difference between the points

The difference is calculated as follows:

Difference = Highest - Lowest

Difference = 5764\ feet - 7\ feet

Difference = 5757\ feet

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So, the bicycle looks like the one in the picture below.

now, the circumference of the smaller wheel, will just be C = 2πr, with a radius of "r".

we also know that the large wheel has a circumference that is 9 feet larger than the small one, so, since the small one has a circumference of 2πr, then the large one will have a circumference of 2πr + 9.

after Thomas cycled for a while, the large did 500 revolutions, or times around, whilst the small one did 1400, since it's smaller.  On that time, they covered however, the same amount of ground, since they're on the same bike.

The amount covered by the small one in 1400 cycles, is 1400(2πr), that's how much ground it covered.

The amount covered by the large one in 500 cycles, is 500(2πr + 9).

And we know that ground covered, is the same for both, therefore, we also know that   1400(2πr)  =  500(2πr + 9).

\bf \stackrel{small~wheel}{1400(2\pi r)}~~=~~\stackrel{large~wheel}{500(2\pi r+9)}\implies 14(2\pi r)=5(2\pi r+9)
\\\\\\
28\pi r=10\pi r+45\implies 18\pi r=45\implies r=\cfrac{45}{18\pi }
\\\\\\
\boxed{r=\cfrac{5}{2\pi }}

so, how much ground did they cover anyway?

well, we could use either, since we know what the radius is, hmmmm let's use say the small wheel's circumference,

\bf 1400(2\pi r)\implies 1400\left(\underline{2\pi }\cdot \cfrac{5}{\underline{2\pi }}  \right)\implies 1400(5)\implies \stackrel{feet}{7000}

8 0
3 years ago
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Step-by-step explanation:

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